Ratio test
Ratio test
Lessons
Notes:
Note *Let $\sum a_n$ be a series. Then we say that
$R=$$\lim$_{n →$\infty$} $\mid \frac{a_{n+1}}{a_n}\mid$
Where:
1. If $R$ < $1$, then the series is convergent (or absolutely convergent)
2. If $R$ > $1$, then the series is divergent
3. If $R=1$, then the series could either be divergent, or convergent
Basically if $R=1$, then the ratio test fails and would require a different test to determine the convergence or divergence of the series.

2.
Convergence & Divergence of Ratio Test
Use the Ratio Test to determine if the series converges or diverges. If the ratio test does not determine the convergence or divergence of the series, then resort to another test.